Predicting different turbulent mixing problems with the same k–ɛ model and model coefficients

Abstract

In the foreseeable future, the Reynolds-averaged Navier–Stokes (RANS) method will remain the most viable approach for simulating practical flows. The RANS method mainly comprises two parts: a physical model and model coefficients. Hitherto, although researchers have made great effort to improve them, there is still much room for improving the satisfaction of RANS prediction. Given an available but possibly non-accurate physical model, is it possible to achieve a satisfactory RANS prediction? Our recent work on determination of k–L mixing model coefficients [Zhang et al., J. Fluid Mech. 905, A26 (2020)] sheds light on this problem. In that study, a satisfactory RANS prediction is achieved by systematically setting the values of model coefficients to match the given model. In this paper, we further extend this methodology to the widely used k–ɛ model. Consequently, with the same k–ɛ model and the same model coefficients, we successfully predict different turbulent mixing problems induced by various interface instabilities, which broadly occur in both nature and engineering. The investigated problems include both basic mixing problems, e.g., classical Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz mixing, and complex mixing problems, e.g., reshocked RM mixing, RT mixing with initial tilted interface, and spherical implosion mixing. The successful predictions of the k–ɛ model, as well as those of the k–L model, indicate that the idea mentioned above may be applied to other RANS models and bring hope for predicting engineering problems with the same physical model and the same model coefficients.